# As can be seen through Fig there existed a

As can be seen through Fig. 3 there existed a negative covariance between the primary deficit and the rates of return on debt. This negative covariance is observed in almost all RG7112 under review. This result is in consonance with that observed by Angeletos (2002), Barro (2003), and Nosbusch (2008). In other words, management of the returns of the securities can protect the budget from changes in public sector\'s borrowing requirements.
It is important to highlight that the main objective of the Brazilian National Treasury is focused on two points: (i) gradually replacing floating rate bonds with fixed rate or inflation-linked instruments as a way of reducing market risk; and (ii) increasing the average maturity of outstanding debt as a manner of reducing the refinancing risk. As can be seen from Fig. 4 the average maturity, as well as the long term maturity debt (longer than 1 year – Mat), is increasing over time. Regarding the public debt profile, it is observed that the strategy of increasing the participation of securities indexed to the price index (IPCA – I_IPCA) and decreasing securities indexed to the Selic rate (I_Selic) is working. On the other hand the share of fixed-rate securities (Fix) remained relatively stable in the period.
With the objective of observing whether the strategy adopted by the Brazilian National Treasury of extending the average maturity of public debt and improving the public debt profile helped the fiscal insurance, an empirical analysis is made. The baseline model is a result of the relationship of the form:where is a vector of the performance indicators for the debt management; and is a vector of the main public debt indexing factors:
Based on the equation above Ordinary Least Squares (OLS) and Generalized of Method of Moments are used for regressions. The reason for the use of these methods is that they permit observing the significance of each coefficient on each variable considered in the empirical model. Therefore, the identification of the relevant variables is crucial for recommendation for debt management. Contrary to the manner suggested by Faraglia et al. (2008) the use of time series for the analysis in the Brazilian case is not a drawback. Key variables such as maturity of debt change over time. In a general way OLS models are not efficient from macroeconomic time series. The traditional problems of serial autocorrelation, heteroskedasticity, or non-linearity imply the necessity of the use of other methods such as GMM (see Hall, 2005).

Empirical evidence
Table 1 shows the results of regressing our performance indicators on the average maturity of debt and public debt indexing factors (I_Selic, I_IPCA, and Fix). Contrary to standard argument that issuing longer maturity debt helps to improve fiscal insurance, most of the results in both OLS and GMM regressions (see Table 1) present positive coefficients on maturity although without statistical significance. The results regarding the share of the federal public debt with fixed rate bonds are mixed in terms of the sign and only in a few cases the coefficients are significant. The sign of the coefficients on share of the federal public debt linked to both IPCA and Selic are positive in most of the models. Therefore, this result denotes that it does not matter if the government issues indexed to the inflation or the interest rate to improve fiscal insurance. In short, the results present very little relationship between fiscal insurance and public debt management (public debt profile and average maturity of public debt).
With the intention of checking if longer maturity debt can improve the fiscal insurance, the variable average maturity of public debt was substituted by average maturity longer than 12 months (see Table 2). As pointed out by Nosbusch (2008) a greater proportion of long-term government securities can provide a hedge against shocks to the economy due to the fact that these securities are more sensitive to changes in the interest rates. The results indicate that there was no difference regarding the statistical significance on the coefficients. However, the sign of the coefficients became mixed, which in turn suggests that an increase in longer maturity can affect the fiscal insurance. The results regarding the other variables in the models did not change considerably from those observed in the previous model.